The simple answer is no.
According to House of Commons briefing paper No 07212 on the European Union Referendum Bill 2015-16:
“This Bill requires a referendum to be held on the question of the UK’s continued membership of the European Union (EU) before the end of 2017. It does not contain any requirement for the UK Government to implement the results of the referendum, nor set a time limit by which a vote to leave the EU should be implemented. Instead, this is a type of referendum known as pre-legislative or consultative [our emphasis] which enables the electorate to voice an opinion which then influences the Government in its policy decisions.”
In other words, it’s entirely up to the Government what happens next – and anything that happens must be approved by our elected representatives in the House of Commons, as well as the House of Lords.
NB the referendums held in Scotland, Wales and Northern Ireland in 1997 and 1998 were examples of this type, where opinion was tested before legislation was introduced. In contrast, the legislation which provided for the referendum held on AV in May 2011 would have implemented the new system of voting without further legislation.